CN109918819A - A kind of extensive bridge network estimation method based on Bayesian network - Google Patents
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Abstract
The invention proposes a kind of extensive bridge network estimation method based on Bayesian network, with ORDER-II and dijkstra's algorithm and vulnerability thought, condition state grade and intercity range information using network Bridge realize extensive bridge network total reliability assessment and key road segment bridge recognition.It converts the NP-hard problem for solving extensive bridge Reliability of Network under claimed accuracy and solves the most probable failure combination of bridge and network-in-dialing state issues.This passes through the assessment to certain national highway bridge network comprising 1772 bridge blocks, it was demonstrated that method proposed by the invention can assess extensive bridge network total reliability with vulnerability index, and can effectively pick out each section bridge relative importance.The present invention can directly efficiently assess large bridge network.
Description
Technical field
The present invention relates to a kind of method of civil engineering bridge network evaluation, and in particular to a kind of based on Bayesian network
Extensive bridge network estimation method.
Background technique
For bridge as part the most fragile in basic facility transportation network, safety is to guarantee highway quickly unimpeded fortune
Capable key is of great significance to guarantee infrastructure transportation network safe operation or even Regional Economic Development.According to traffic
" the 2018 traffic transport industry statistical communique of development " of Department of Transportation's publication, by the end of the year 2018, highway in China bridge 83.25 ten thousand
Seat, 5225.62 myriametres are the bridge big countries of the first in the world.
In bridge life cycle management, the construction period only accounts for the full-bridge service life less than 10%, other are curing period.However, bridge
Beam moves back during long service due to being influenced aging, service performance and security performance occur by factors such as load and environment
The problems such as change.According to statistics, 40% servicing bridges active time has been more than 20 years in Chinese Highway road network, industrial grade three
The bridge in spite of illness nearly 30% of class, four classes, unsafe bridge quantity reach 15% (about 100,000).With the bridge number for stepping into the maintenance maintenance phase
Measure increasing, the safe condition of bridge structure can not be ignored.
According to Department of Transportation's " about several opinions for further strengthening highway bridge maintenance management " (road hair of handing over to the collective or the state
[2013] No. 321) documentation requirements, " determining comprehensive inspection of bridge technology situation, three Nian Yici should be no less than ".Therefore, national
Each province and city can all generate the magnanimity detection monitoring information for bridge structure every year.And existing traffic infrastructure is detected, is commented
Estimate and carried out as unit of single seat bridge with maintenance strategy formulation, limits between each bridge interconnecting spatially, no
Conducive to the unified management of more infrastructure architectures in region, cause when safety warning occur in more bridge blocks, it can not be quickly quasi-
Really exclude security risk.It is high for the maintenance and repair expense summation of all bridges in region simultaneously.According to Department of Transportation
" national turn pike statistical communique in 2017 " statistics of publication, in 2017 years, national Toll Road income is
5130.2 hundred million yuan, 9156.7 hundred million yuan of gross expenditure, maintenance and operation management pay 1161.5 hundred million yuan, accounting 12.7%.Cause
How this, evaluate the relative importance of section bridge in network, be of great significance.
The bridge network Reliability assessment method being widely used at present has: State enumeration method, series and parallel connection method, event tree method
Deng.Due to for a network containing m unreliable components (bridge), status number 2m.With bridge network size
Expand, preceding method will inevitably fail, and be only applicable to the small-scale bridge network model containing a small amount of bridge.Therefore urgently
A kind of quickly and effectively extensive bridge network estimation method based on Reliability of Network need to be developed.
Summary of the invention
In order to solve the problems, such as extensive bridge network evaluation, the present invention provides a kind of based on Reliability of Network the present invention
Extensive bridge network estimation method, can rapidly and accurately exclude security risk.
A kind of the technical solution adopted by the present invention to solve the above technical problem are as follows: extensive bridge based on Bayesian network
Beam network estimation method, steps are as follows:
Step 1: it is overlapping with hum pattern that bridge network being considered as topological diagram, bridge network physical model is established, wherein opening up
Flutter graph model include by network route and the side that is simplified to respectively of route intersection point and node, information graph model include in network
The condition state grade of each edge lengths and thereon bridge；
Step 2: calculate monomer bridge failure probability, using in AASHTO standard criterion reliability algorithm and system because
Son converts the condition state grade of bridge on network to the reliability and failure probability of bridge entirety, Pf=Φ (- βb),
In formula, PfFor the failure probability of bridge, βbFor bridge RELIABILITY INDEX, the design safety grade of bridge RELIABILITY INDEX and structure
And technology status grade is related；
Step 3: calculating the failure probability of equivalent bridge, the bridge in network in same edge is considered as serial system, and fixed
The adopted serial system is equivalent bridge, while calculating its reliability and failure probability,In formula, PEi
Indicate the failure probability of equivalent bridge, Pf(i,j)Indicate the failure probability of upper j-th of the bridge of equivalent bridge i；K is equivalent bridge i packet
The entity bridge sum contained；
Step 4: three layers of Bayesian network model of most original are considered using ORDER-II algorithm and dijkstra's algorithm, point
Not Ji Suan in precision prescribed lower network all equivalent bridges most probable state combination and various combination lower network connection feelings
Condition, and then network total reliability is calculated,In formula, C is the probability of network-in-dialing, EiIt is complete
I-th of event of event group E, wherein E contains all failure combinations that component in network is under different conditions, and P (C | Ei)
For known event EiThe probability of network-in-dialing, M are the total quantity of network state；
Step 5: in conjunction with the influence failed to network total reliability of failure probability and its of bridge, calculating its vulnerability and refer to
Mark, and then assess its relative importance
In formula, VI is the vulnerability index of bridge i,Network is not connected in the case where for known bridge i failure
Probability, Pf(Bi) be bridge i failure probability,For the probability that bridge i and network fail simultaneously, and P (C | Bi) it is
Know the probability of network-in-dialing in the case that bridge i fails.
Beneficial effects of the present invention: bridge network estimation method of the invention, using bridge network technology status assessment etc.
Grade and road section length information calculate Reliability of Network and bridge vulnerability based on Bayesian network, and method is easy to use, calculates essence
Degree is high and can be realized the relative importance of identification section bridge, the robustness of the method for the present invention and highly reliable, can be quick
Security risk is accurately excluded, provides skill with the assessment of monomer bridge service state and operation maintenance in network for bridge network is whole
Art support.
Detailed description of the invention
Fig. 1 ORDER-II-Dijkstra algorithm flow chart；
Fig. 2 includes the national highway network of bridge；
Fig. 3 is the construction time limit and evaluation grade statistical chart of Fig. 2 network Bridge；
Fig. 4 is Fig. 2 network jackshaft beam type and evaluation grade statistical chart；
Fig. 5 is national highway bridge network topological diagram and information figure layer overlay chart；
Fig. 6 is the physical model figure of Fig. 5；
Fig. 7 is entity bridge evaluation grade statistical information figure on each side of Fig. 5；
Fig. 8 is the failure probability figure of 68 equivalent bridges on national highway bridge network；
Fig. 9 is the vulnerability indicatrix of 68 equivalent bridges on national highway bridge network；
Specific embodiment
Below according to Figure of description citing, the present invention will be further described:
Embodiment 1
A kind of extensive bridge network estimation method based on Bayesian network: it establishes containing certain amount side and node
Topological network, wherein side and node are respectively the route and route intersection point in network；It will by edge lengths each in network and thereon
The Information Level and topological network of the condition state grade composition of bridge are laminated simultaneously.
The failure probability of bridge can be obtained by its RELIABILITY INDEX
Pf=Φ (- βb) (1)
In formula, PfFor the failure probability of bridge, βbFor the RELIABILITY INDEX of bridge.Bridge RELIABILITY INDEX and structure are set
It counts security level and technology status grade is related.According to highway engineering structural reliability design unified standard (GB/T 50283-
1999), the design safety grade of highway bridge structure reflects structure and destroys issuable severity of consequence, can be according to
Bridges and culverts structure is divided, such as table 1.Simultaneously under the conditions of ductile fracture, the bridge structure component based on AASHTO standard is reliable
The one-to-one relationship spent between index and each security level and technology status grade is as shown in table 2.Based on AASHTO standard
The value of the system factor of definition is as shown in table 3, can be by each member reliability level promotion to system reliability level.
1 highway engineering structure design safety grade of table
Table Bridge 2 girder construction member reliability index evaluation standard
The value of system factor in table 3AASHTO
If solid bridge beam-like state TiFor Boolean variable, i.e.,
Therefore, for a network with the m bridges that can fail, the number of states of bridge network entirety is 2m.For letter
Change computation complexity, do not consider the failure of road, i.e., bridge network Bridge be uniquely can failure member.Defining equivalent bridge is
The serial system of bridge composition in network in same edge, calculates its failure probability:
In formula, PEiIndicate the failure probability of equivalent bridge, Pf(i,j)Indicate that the failure of upper j-th of the bridge of equivalent bridge i is general
Rate；K is the entity bridge sum that equivalent bridge i includes.Therefore, the failure probability of equivalent bridge and the quantity of bridge thereon and
The failure probability of each bridge is related.
Extensive bridge Reliability of Network is calculated using three layers of Bayesian network model of most original.
In formula, BN is bridge network, and NP is the node pair in network, and B is bridge, and R is Reliability of Network.It is former based on reprimand is held
Reason, bridge Reliability of Network are defined as
In formula, { f1,f2,…,fqBe network minimal path set, while above formula can be reduced to
It is not connected between arbitrary node pair if the failure for defining any bridge in network will lead to, bridge network is not
Otherwise connected state is connected state, and then can acquire its connectivity reliability by network-in-dialing probability.Therefore network can be connected
More terminal problems are converted into single terminus problem in general character judgement.Meanwhile the connected probability of network becomes owning in network
While bridge is in variant state the probability of network-in-dialing and:
And then it is decomposed into
In formula, C is the probability of network-in-dialing, EiFor i-th of event of self-contained mode E, wherein E is contained in network
Component is in all failure combinations under different conditions, and P (C | Ei) it is known event EiThe probability of network-in-dialing, M are network state
Total quantity.
Wherein ORDER-II algorithm does not consider network-in-dialing state, finds using most rickle principle complete under claimed accuracy
Most probable event in event group E.Wherein apply formula
The failure probability of equivalent bridge is converted into the weight in algorithm, since the conversion weight is with the increasing of failure probability
Add monotone decreasing, therefore by equivalent bridge according to w (EqBi)≥w(EqBj) (i > j) sequence arrangement, that is, failure probability passs
The sequence arrangement subtracted.Most rickle principle is then applied, every step by adding the equivalent bridge SS in part theretoi-{eL (SSi)}+
{n(eL(SSi)) and SSi+{n(eL(SSi)), and most rickle is updated, the failure for taking the root node of most rickle to obtain for the step
Combination, while deleting the new heap formed after the root node of heap and being calculated for next cycle.Until obtaining under expected probability α
The most probable preceding a kind failure combination of network.
Dijkstra's algorithm is used to solve the shortest path from a vertex to remaining each vertex.It is by by vertex set
The vertex set (V-N) for being divided into the vertex set N for having found out shortest path and being not determined by shortest path, and define wherein one
A vertex is source node, and by comparison source node, the last bit node of the length on each vertex and source node into N is again in (V-N)
The path length on any vertex in (V-N) updates the shortest path in (V-N), and successively that the path in (V-N) is minimum
It is worth corresponding node to be added in N, until (V-N) is empty set.Dijkstra algorithm passes through on the basis of dijkstra's algorithm
Change weight matrix, and then change the source node of algorithm, finds shortest path in network between all terminus pair and most short
Distance, to judge the connected state of network.When searching node i to the shortest distance between other all nodes, general first
The transformation of unit matrix A row or rank transformation are converted into matrix A ':
In formula,Row transformation between the i-th row and the 1st row,Between i column and the 1st column
Rank transformation.Weight matrix can be converted using following formula later
W'=A'WA'(11)
In formula, W is the weight matrix of network, the actual range being taken as between node.Therefore, it is first obtained by ORDER-II
The most probable state of network, and then application dijkstra's algorithm calculates the connection situation of each state lower network entirety, using formula
(8) connected probability of network can be acquired.
As shown in figure 1, PEiFor the failure probability of equivalent bridge i；M is the quantity of equivalent bridge in network；N is nodes
Quantity；V is the set of all nodes in network；A is network most probable failure combination；S is all equivalent bridges in network according to w
(EqBi)≥w(EqBj) (i > j) sequence set；S (i) is i-th of amount in S；α is algorithm accuracy；For equivalent bridge weight；w(SSi) it is SSiIn equivalent bridge weight and；SSiFor the subset of S,
Meet w (SSi)≥w(SSj) (i > j), the equivalent bridge set of table non ageing；P(SSi) it is SSiIn equivalent bridge be failure,
His equivalent bridge is the probability being on active service；eL(SSi) it is SSiLast position；n(EqBi) be S in equivalent bridge i next bit；
SSi-{eiIt is SSiDelete eiSet；SSi+{eiIt is SSiAdd eiSet；N is shortest path node collection；D (j) is from i
Point arrives the shortest distance of source point；U is node nearest from source point in V-N；Dis (j) is node j and eL(N) node direct range.
The failure probability that the vulnerability index of bridge network combines network Bridge fails with it to Reliability of Network
It influences, to judge the relative importance of bridge, identifies the key road segment bridge in network.Therefore, on route after bridge failure
Without other alternative routes, vulnerability index is
In formula, VI is the vulnerability index of bridge i,Network is disconnected in the case where for known bridge i failure
Probability, Pf(Bi) be bridge i failure probability,For the probability that bridge i and network fail simultaneously, and P (C | Bi) it is known
The probability of network-in-dialing in the case that bridge i fails.Therefore, the lesser bridge of vulnerability index is to the safe and reliable of network entirety
It is even more important.
Step 1: the building of bridge network physical model.As shown in figure 5, bridge network is considered as topological diagram and hum pattern
Overlapping, wherein topological graph model includes the side being simplified to respectively by the route in network with route intersection point and node, information artwork
Type includes each edge lengths and the condition state grade of bridge thereon in network；
Step 2: calculating monomer bridge failure probability.Using in AASHTO standard criterion reliability algorithm and system because
Son converts bridge entirety for the condition state grade of bridge on network in conjunction with the design safety class information of bridge
Reliability and apply Pf=Φ (- βb) formula calculates its failure probability；
Step 3: calculating the failure probability of equivalent bridge.Bridge in network in same edge is considered as serial system, and fixed
The adopted serial system is equivalent bridge, while calculating its reliability and failure probability
Step 4: calculating network total reliability index.Most original is considered using ORDER-II and Dijkstra algorithm
Three layers of Bayesian network model, calculate separately all equivalent bridges in precision prescribed lower network most probable state combination and not
With the connection situation of combination lower network, and then apply formulaCalculate network total reliability；
Step 5: assessing each section bridge relative importance.It fails with it and integrally may be used to network in conjunction with the failure probability of bridge
By the influence of degree, its vulnerability index is calculatedAnd then assess its relative importance.
Embodiment 2
Specific embodiments of the present invention, by combining the analysis and assessment of certain national highway bridge network to be illustrated.
As shown in Fig. 2, national highway bridge network total kilometrage is 7089km, 1 capital radioactive ray, 8 north and south longitudinal direction are covered
Line, 5 thing x wires and 3 connecting lines include 11 cities and 1772 bridge blocks.As shown in figure 3,1772 bridge blocks
In more than 60% Years Of Service be less than 20 years；As shown in figure 4, be more than simultaneously 80% Bridge Evaluation grade be 1 class and 2 classes, place
In preferable service state.
Step 1: building bridge network physical model, as shown in Figure 6.Bridge network is considered as to the weight of topological diagram and hum pattern
It is folded, as shown in fig. 6, wherein topological graph model include by the route and the side that is simplified to respectively of route intersection point and node in network,
Information Level includes each edge lengths and the condition state grade of bridge thereon in network, as shown in Figure 7；
Step 2: using AASHTO standardize in reliability algorithm and system factor, in conjunction with the design safety grade of bridge
Information converts the reliability of bridge entirety for the condition state grade of 1772 bridge blocks on network and using Pf=Φ (-
βb) formula calculates its failure probability；
Step 3: finding 68 equivalent bridges in network, in conjunction with the failure probability of its bridge of being taken in, it is reliable to calculate it
Degree and failure probabilityAs shown in Figure 8；
Step 4: considering three layers of Bayesian network model of most original using ORDER-II and dijkstra's algorithm, count respectively
The most probable state combination and the connection situation of various combination lower network of 68 equivalent bridges in 99.9% precision lower network are calculated,
And then apply formulaCalculating network total reliability is 0.99439；
Step 5: in conjunction with the influence failed to network total reliability of failure probability and its of equivalent bridge, calculating and exist
Its vulnerability index under 99.9% precisionAs shown in figure 9, and then assessing its relative importance.
This appraisal procedure can accurately identify that Tumen in network-Hunchun section bridge is most important, to network whole with people
Common sense, which differentiates, unanimously demonstrates the accuracy of the proposed method of the present invention.
Claims (1)
1. a kind of extensive bridge network estimation method based on Bayesian network, which is characterized in that method and step is as follows:
Step 1: it is overlapping with hum pattern that bridge network being considered as topological diagram, establishes bridge network physical model, wherein topological diagram
It includes each side in network that model, which includes by side and node, information graph model that the route in network is simplified to respectively with route intersection point,
The condition state grade of length and thereon bridge；
Step 2: monomer bridge failure probability is calculated, using the reliability algorithm and system factor in AASHTO standard criterion,
Convert the condition state grade of bridge on network to the reliability and failure probability of bridge entirety, Pf=Φ (- βb), formula
In, PfFor the failure probability of bridge, βbFor bridge RELIABILITY INDEX, the design safety grade of bridge RELIABILITY INDEX and structure with
And technology status grade is related；
Step 3: calculating the failure probability of equivalent bridge, the bridge in network in same edge is considered as serial system, and defining should
Serial system is equivalent bridge, while calculating its reliability and failure probability,In formula, PEiIt indicates
The failure probability of equivalent bridge, Pf(i,j)Indicate the failure probability of upper j-th of the bridge of equivalent bridge i；The equivalent bridge i of k includes
Entity bridge sum；
Step 4: considering three layers of Bayesian network model of most original using ORDER-II algorithm and dijkstra's algorithm, count respectively
The most probable state combination and the connection situation of various combination lower network for calculating all equivalent bridges in precision prescribed lower network, into
And network total reliability is calculated,In formula, C is the probability of network-in-dialing, EiFor self-contained mode
I-th of event of E, wherein E contains all failure combinations that component in network is under different conditions, and P (C | Ei) it is known
Event EiThe probability of network-in-dialing, M are the total quantity of network state；
Step 5: in conjunction with the influence failed to network total reliability of failure probability and its of bridge, its vulnerability index is calculated,
And then assess its relative importance
In formula, VI is the vulnerability index of bridge i,Network is disconnected general in the case where for known bridge i failure
Rate, Pf(Bi) be bridge i failure probability,For the probability that bridge i and network fail simultaneously, and P (C | Bi) it is known bridge
The probability of network-in-dialing in the case that i fails.
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| CN113094843A (en) * | 2021-04-30 | 2021-07-09 | 哈尔滨工业大学 | Solving method for conditional probability of beam bridge evaluation based on Bayesian network |
| CN113743831A (en) * | 2021-11-03 | 2021-12-03 | 深圳市城市交通规划设计研究中心股份有限公司 | Bridge network comprehensive performance evaluation method and device and storage medium |
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